We have different types of triangles existing such as an acute, obtuse, right triangle. Before understanding 30-60-90 formulas, let us first recall what is a 30-60-90 triangle. 30-60-90 is one of the special right triangles where the three interior angles measure 30°, 60°, and 90°. Right triangles with 30-60-90 interior angles are known as special right triangles i.e, their sides and angles are predictable and consistent.
All 30-60-90 triangles are similar.
Two 30-60-90 triangles sharing a long leg form an equilateral triangle.
Let us understand 30-60-90 Formula using solved examples in the following section.
What is the 30-60-90 Formula?
A 30-60-90 degree triangle is a special right triangle, so its side lengths are always consistent with each other. The ratio of the sides follow the 30-60-90 triangle ratio given by the 30-60-90 Formula as,
1 : 2 : √3
Thus, for a 30-60-90 triangle, the dimensions of the sides can be given as:
x = Short side (opposite the 30 degree angle)
2x = Hypotenuse (opposite the 90 degree angle)
x√3 = Long side (opposite the 60 degree angle)
These three special rules can be considered the 30-60-90 triangle theorem and are unique to these special right triangles:
The hypotenuse (the triangle's longest side) is always twice the length of the short leg.
The length of the longer leg is the short leg's length times √3.
If you know the length of any one side of a 30-60-90 triangle, you can find the missing side lengths.
Let's solve some examples using 30-60-90 Formula
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